Nicholas Weaver wrote:
"In order to believe that PA has a model we need to believe
in structures of type omega. For example, I have suggested a
structure involving marks on paper. There is no need to posit
the existence of natural numbers as some special kind of abstract
entities. You can doubt that omega structures exist but this is
not a doubt about platonism."
Alas, one person's marks on papers are another's abstract object smelling
foully of Platonism. As Weaver perfectly well knows, a sheet of paper holds
only finitely many marks. An example of an outstanding mathematician who
finds the marks-on-paper no help is Jack Schwartz who has written on the
matter on FOM and elsewhere.
Martin